3 Answers
3

This is a dimetric projection (a special case of the axonometric projection) with the horizontal axes at tan-1(0.5) ≈ 26.565° (an isomeric projection would have them at 30°, by the way) from the horizontal line.

It's commonly called "isometric projection", but it isn't exactly one.

EDIT:

A simple transformation matrix for this one, assuming the x and y axes lie on the horizontal plane, the z axis points up and the x axis points to the right after projection is

| 1 -1 0 |
| 0.5 0.5 n |
| 0 0 0 |

... with n (the vertical scale factor) being usually chosen arbitrary somewhere between 0.75 and 1.0 (the "true" one would be about 1.118).

This projection gets chosen over the true isomeric one because of this simple transformation matrix, and the fact you can more easily produce matching tiles for it.

It's isometric projection or perspective. Isometric perspective can work very well with a 2D game, and there is the example of the Flexible Isometric Free Engine which is a 2D engine, with an isometric view (though as it is flexible, that is not forced).

Yes, they are 2D sprites. These sprites, as those in Diablo I, II, Starcraft I, Warcraft II as just a few (Blizzard) examples, were pre-rendered from a 3D content creation package like 3DSMax, Maya or Lightwave. That means you have a camera swivelling around them taking every possible frame of animation from a set number of camera angles. So if you character had 10 animations of 40 frames each, to be rendered from 16 different angles, that would take you to a total of 6400 frames of animation for just that character alone. However it allows you to use 2D instead of 3D in your game, and the characters are lit as they were when rendered, which usually gives them a very particular look. These are then imported into the game (usually as spritesheets) and rendered as 2D sprites.

Generally these sort of sprites are touched up by hand after the rendering process, using a raster package like Photoshop or Cosmigo, particularly when quite small as in Age of Empires I & II.

As for the perspective, strictly (mathematically) speaking I agree with Martin Sojka, whereas in broader terms, most gamers and game developers would refer to this as isometric. I tend to favour strictness of terminology; kudos to you Martin.